Question: {r} values in eigenvectors

Hello everyone,

I'm trying to symbolically diagonalize a 5x5 matrix in Maple. I can determine the eigenvalues for my matrix, but when it comes to evaluating the eigenvectors, Maple gives me the following results:

eigenvalues(A): -a + u, a + u, u, u, u

eigenvectors(A): [a + u, 1, {r}], [-a + u, 1, {r}], [u, 5, {r, r, r, r, r}]

I don't understand why I'm getting {r} in the eigenvectors. How can I display the eigenvectors for my matrix A?

Thank you in advance for your answers !

5x5

 

restartNULL

with(linalg)

[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, coldim, colspace, colspan, companion, concat, cond, copyinto, crossprod, curl, definite, delcols, delrows, det, diag, diverge, dotprod, eigenvals, eigenvalues, eigenvectors, eigenvects, entermatrix, equal, exponential, extend, ffgausselim, fibonacci, forwardsub, frobenius, gausselim, gaussjord, geneqns, genmatrix, grad, hadamard, hermite, hessian, hilbert, htranspose, ihermite, indexfunc, innerprod, intbasis, inverse, ismith, issimilar, iszero, jacobian, jordan, kernel, laplacian, leastsqrs, linsolve, matadd, matrix, minor, minpoly, mulcol, mulrow, multiply, norm, normalize, nullspace, orthog, permanent, pivot, potential, randmatrix, randvector, rank, ratform, row, rowdim, rowspace, rowspan, rref, scalarmul, singularvals, smith, stackmatrix, submatrix, subvector, sumbasis, swapcol, swaprow, sylvester, toeplitz, trace, transpose, vandermonde, vecpotent, vectdim, vector, wronskian]

(1.1)

A := Matrix([[0, 1, 0, 0, 0], [(gamma-1)*H-u^2-a^2, (3-gamma)*u, -(gamma-1)*v, -(gamma-1)*w, gamma-1], [-u*v, v, u, 0, 0], [-u*w, w, 0, u, 0], [u*((gamma-2)*H-a^2), H-(gamma-1)*u^2, -(gamma-1)*u*v, -(gamma-1)*u*w, gamma*u]])

Matrix(%id = 18446746202416421574)

(1.2)

eigenvalues(A)

u+(-gamma*u^2-gamma*v^2-gamma*w^2+2*H*gamma-a^2+u^2+v^2+w^2-2*H)^(1/2), u-(-gamma*u^2-gamma*v^2-gamma*w^2+2*H*gamma-a^2+u^2+v^2+w^2-2*H)^(1/2), u, u, u

(1.3)

V := sqrt(u^2+v^2+w^2)

(u^2+v^2+w^2)^(1/2)

(1.4)

H := (1/2)*V^2+a^2/(gamma-1)

(1/2)*u^2+(1/2)*v^2+(1/2)*w^2+a^2/(gamma-1)

(1.5)

eigenvalues(A)

-a+u, a+u, u, u, u

(1.6)

eigenvectors(A)

[-a+u, 1, {r}], [a+u, 1, {r}], [u, 3, {r, r, r}]

(1.7)

``

Download maps.mw

Please Wait...